Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 45

Applications to Solid State

4.97 Thermal Expansion and Heat Capacity

(Princeton)

a) Findthe temperaturedependence ofthe thermalexpansion coefficient

if the interaction between atoms is described by a potential

b)

where is a small parameter.

Derive the anharmonic corrections to the Dulong–Petit law for a po-

tential

where is a small parameter.

4.98 Schottky Defects (Michigan State, MIT)

N atoms from a perfect crystal of total number of atoms are displaced to
the surface of the crystal. Let be theenergy needed todisplace oneatom
from the bulk of the crystal to the surface. Find the equilibrium number
of defects N at low temperatures assuming

4.99 Frenkel Defects (Colorado, MIT)

N atoms are arranged regularly to form a perfect crystal. If one replaces
atoms among them from latticesites to interstices of the lattice, this